Methods and apparatus to calibrate micro-electromechanical systems

ABSTRACT

Methods and apparatus to calibrate micro-electromechanical systems are disclosed. An pressure sensor calibration apparatus includes a pressure chamber in which a first pressure sensor is to be disposed; one or more first sensors to measure a first capacitance value from the first pressure sensor from a physical test performed; the one or more first sensors to measure a second capacitance value from a first electrical test performed on the first pressure sensor; and a correlator to determine correlation coefficient values based on the first capacitance value determined during the physical test on the first pressure sensor and the second capacitance value determined during the first electrical test on the first pressure sensor; and a calibrator to determine calibration coefficient values to calibrate a second pressure sensor based on the correlation coefficient values and a third capacitance value determined during a second electrical test on the second pressure sensor.

FIELD OF THE DISCLOSURE

This disclosure relates generally to micro-electromechanical systems,and, more particularly, to methods and apparatus to calibratemicro-electromechanical systems.

BACKGROUND

Micro-electromechanical systems (MEMS) such as, for example, pressuresensors are relatively nonlinear devices. Based on this nonlinearity anddifferences between pressure sensors, typically, each pressure sensor isindividually calibrated. Such an approach may increase the capital costof equipment used to calibrate the pressure sensors and/or increase thetime dedicated to calibrating each of the pressure sensors.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of an example system used during anexample testing phase to calibrate micro-electromechanical systems inaccordance with the teachings of this disclosure.

FIG. 2 is a schematic illustration of the example correlator of FIG. 1.

FIG. 3 is a schematic illustration of an example system used during anexample testing phase to calibrate micro-electromechanical systems inaccordance with the teachings of this disclosure.

FIG. 4 is a schematic illustration of an example implementation of theexample calibrator of FIG. 3.

FIG. 5 is an example graph of capacitance versus pressure illustratingresults obtained using the examples disclosed herein.

FIG. 6 is an example graph of capacitance versus voltage illustratingresults obtained using the examples disclosed herein.

FIG. 7 is an example graph of correlation curves generated based onresults obtained using the examples disclosed herein.

FIG. 8 is a flow chart representative of machine readable instructionsthat may be executed to implement the example correlator and the examplecalibrator of FIGS. 1-4.

FIG. 9 is a flow chart representative of machine readable instructionsthat may be executed to implement the correlator of FIGS. 1 and 2 and toperform the processes of FIG. 8 to determine correlation coefficientvalues for different pressure values.

FIG. 10 is a flow chart representative of machine readable instructionsthat may be executed to implement the calibrator of FIGS. 3 and 4 and toperform the processes of FIG. 8 to determine calibration coefficientvalues for a second sensor.

FIGS. 11 and 12 illustrate processor platforms which may execute theinstructions of FIGS. 8-10 to implement the example correlator and theexample calibrator of FIGS. 1-4.

The figures are not to scale. Wherever possible, the same referencenumbers will be used throughout the drawing(s) and accompanying writtendescription to refer to the same or like parts.

DETAILED DESCRIPTION

The examples disclosed herein relate to calibratingmicro-electromechanical systems (MEMS) such as, for example, pressuresensors and/or capacitive based barometric pressure sensors.Specifically, the examples disclosed herein relate to performing testson first pressure sensors during a training phase and calibrating secondpressure sensors during a testing phase using correlation coefficientvalues determined during the training phase. By taking such an approach,the examples disclosed herein enable the efficient calibration of alarge quantity of pressure sensors based on correlation coefficientvalues determined by testing a lesser number of pressure sensors. Assuch, the examples disclosed avoid the time-consuming process ofcalibrating pressure sensors by performing a pressure sweep on eachpressure sensor positioned within a pressure chamber.

In some examples, the training phase includes performing physical andelectrical tests on the first pressure sensors. The physical test(s) mayinclude exposing the first pressure sensors to various pressures (e.g.,performing a pressure sweep) and determining the resultant capacitancevalue(s). In some examples, Equation 1 is used to account for thecapacitance of the first pressure sensor at ambient pressure or, moregenerally, is used to relate pressure and capacitance values determinedduring the physical test, where C_(p) _(x) corresponds to thecapacitance at a particular pressure and C_(p) _(=1013 hPa) correspondsto the capacitance at 1013 hecotopascals (hPa).f(C _(P))=C _(P) _(x) −C _(p) _(=1013 hPa)   Equation 1:

In some examples, the electrical test(s) includes applying variousvoltages (e.g., performing a voltage sweep) to the first pressuresensors and determining the resultant capacitance value(s). The voltagesapplied during the electrical test(s) may be direct current (DC)voltage. In some examples, Equation 2 is used to account for thecapacitance of the first pressure sensor when a minimum voltage (e.g.,0V) is being applied to the first pressure sensor or, more generally, isused to relate voltage and capacitance values determined during theelectrical test(s). Referring to Equation 2, C_(min) corresponds to theminimum capacitance value (e.g., at 0 volts) and C_(min+δV) correspondsto the capacitance at V=V_(min)+δV.

$\begin{matrix}{{f\left( C_{v} \right)} = {\sqrt{\frac{C_{{m\; i\; n} + {\delta\; v}}}{C_{m\; i\; n}}} - 1}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

Based on the pressure and capacitance values determined during thephysical tests and the associated voltage and capacitance valuesdetermined during the electrical tests, in some examples, correlationcoefficient values are determined using a second order polynomialfunction such as, for example, the second order polynomial function ofEquation 3. Referring to Equation 3, b₁ corresponds to a firstcorrelation coefficient, b₂ corresponds to a second correlationcoefficient, b₃ corresponds to a third correlation coefficient, f(C_(p)) corresponds to the capacitance in the physical domain and f(C_(v)) corresponds to the capacitance in the electrical domain.f(C _(p))=b ₁ f(C _(v))² +b ₂ f(C _(v))+b ₃  Equation 3:

After the training phase, the testing phase may be performed. Thetesting phase may include performing electrical tests on second pressuresensors and determining the resultant capacitance value(s). In someexamples, in the testing phase, first and second voltage values areapplied to the second pressure sensors to determine the resultantcapacitances. The first voltage value may be 0-volts and the secondvoltage value may be 3 volts.

Based on the electrical tests performed on the second pressure sensorsduring the testing phase and the correlation coefficient valuesdetermined during the training phase, in some examples, capacitancevalues are determined for the second pressure sensors at differentpressure values without performing physical tests on the second pressuresensors. In other words, capacitance values for the second pressuresensor can be predicted without exposing the second pressure sensor todifferent pressures and determining the resultant capacitances. In someexamples, Equation 4 is used to determine the capacitance value for aselected pressure value for one of the second pressure sensors.C _(p) _(x) =b ₁ f(C _(v))² +b ₂ f(C _(v))+b ₃ +C_(p=1013 hPa)  Equation 4:

To extrapolate the capacitance and pressure values determined usingequation 4, in some examples, a sensor equation fit is used such as, forexample, the sensor equation fit of Equation 5. In some examples, thesensor equation fit is a Levenberg-Marquardt algorithm (LMA). Referringto Equation 5, A_(p) refers to the plate area of the pressure sensorbeing calibrated in the testing phase, ε₀ corresponds to thepermittivity of the free space within the pressure sensor beingcalibrated in the testing phase and x_(p) corresponds to the peak platedisplacement of the pressure sensor being calibrated in the testingphase as defined by Equation 6. Referring further to Equation 5, g₀corresponds to the effective gap (e.g., 545.6 nanometers (nm)) of thepressure sensor being calibrated in the testing phase as defined byEquation 7, δx_(p) corresponds to the displacement adjustment (e.g.,zero offset) of the pressure sensor being calibrated in the testingphase and C_(par) corresponds to the parasitic offset (e.g., 3.2picofarads (pF)) of the pressure sensor being calibrated in the testingphase.

$\begin{matrix}{C = {\frac{A_{P}\epsilon_{0}{{atanh}\left( \sqrt{\frac{x_{p} + {\delta\; x_{p}}}{g_{0}}} \right)}}{\sqrt{g_{0}\left( {x_{p} + {\delta\; x_{p}}} \right)}} + C_{par}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

Referring to Equation 6, a corresponds to the plate radius of thepressure sensor being calibrated in the testing phase and D correspondsto the flexural rigidity of the pressure sensor being calibrated in thetesting phase as defined in Equation 8.

$\begin{matrix}{x_{p} = \frac{P\; a^{4}}{64D}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

Referring to Equation 7, g_(noox) corresponds to the air gap of thepressure sensor being calibrated in the testing phase, t_(ox)corresponds to the thickness of the oxide of the pressure sensor beingcalibrated in the testing phase and εr,ox corresponds to the relativepermittivity of the oxide of the pressure sensor being calibrated in thetesting phase.

$\begin{matrix}{g_{0} = {g_{noox} + \frac{t_{ox}}{\epsilon_{r,{ox}}}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

Referring to Equation 8, E corresponds to Young's modulus, v correspondsto Poisson's ratio and t corresponds to the thickness of the plate(e.g., 8 micrometers(μm)) of the pressure sensor being calibrated in thetesting phase.

$\begin{matrix}{D = \frac{{Et}^{3}}{12\left( {1 - v^{2}} \right)}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

In some examples, to reduce the complexity of the solution, an n^(th)order polynomial fit (e.g., a 4^(th) order polynomial) is performed onthe squared inverted results of the sensor equation fit using, forexample, Equation 9. Referring to Equation 9, C corresponds to thecapacitance determined using Equation 5, a_(i) corresponds to thepolynomial coefficients and {circumflex over (P)} corresponds to thepressure result vector from the polynomial fit. In some examples, thepolynomial fit performed is a 5^(th) order polynomial fit and the outputincludes calibration coefficient values to calibrate the second pressuresensors.

$\begin{matrix}{{\hat{P}(C)} = {\sum\limits_{i = 1}^{n + 1}{a_{i}\left( \frac{1}{C - C_{par}} \right)}^{2{({n - i + 1})}}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

FIG. 1 illustrates an example calibration system 100 that can be used tocalibrate micro-electromechanical systems (MEMS) including pressuresensors in a cost effective and efficient manner. In the illustratedexample, the calibration system 100 includes an example training phase102 that performs physical and electrical tests on a first pressuresensor 104 and uses the results of the physical and electrical tests todetermine correlation coefficient values. While the illustrated exampledepicts one pressure sensor (i.e., the first pressure sensor 104) in thetraining phase 102, in other examples, any number of pressure sensorsmay be used during the training phase 102.

To enable the physical tests to be performed on the first pressuresensor 104 during the training phase 102, in the illustrated example,the calibration system 100 includes an example pressure controller 106,an example pressure sensor and/or gauge 108, an example pressure chamber110 in which the first pressure sensor 104 is disposed and an examplecapacitance sensor 112. In some examples, to perform the physical testson the first pressure sensor 104, the pressure controller 106 sets apressure within the pressure chamber 110 via a pressure value input 113and the pressure gauge 108 measures the actual pressure within thepressure chamber 110 to enable a determination to be made as to whetherthe pressure within the pressure chamber 110 has stabilized and/orwhether the pressure value input 113 and a measured pressure 114 arewithin a threshold of one another.

In some examples, when the pressure within the pressure chamber 110stabilizes and/or when the pressure value input 113 and the measuredpressure 114 are within a threshold of one another, the capacitancesensor 112 measures a first capacitance value(s) 116 from the firstpressure sensor 104 based on the pressure applied. In some examples,results 500 of the physical tests conducted during the training phase102 are plotted on a graph 502 depicted in FIG. 5, where an x-axis 504represents pressure and a y-axis 506 represents capacitance.

Referring back to the example of FIG. 1, the pressure gauge 108 and/orthe capacitance sensor 112 provide or otherwise enable an examplecorrelator 118 to access the measured pressure value(s) 114 and thefirst capacitance value(s) 116 for further processing. In this manner,in some examples, during the training phase 102, the first pressuresensor 104 is exposed to a range of pressures by performing a pressuresweep on the first pressure sensor 104 to enable the first capacitancevalues 116 from the first pressure sensor 104 to be measured using thecapacitance sensor 112. As used herein, the phrase “pressure sweep”refers to exposing a pressure sensor to a plurality of pressure valuesthat may be incrementally or otherwise spaced from one another between afirst pressure value (e.g., 600 hPa) and a second pressure value (e.g.,1013 hPa).

To enable the electrical tests to be performed during the training phase102, in the illustrated example, the calibration system 100 includes anexample first voltage stimulator 120 and the capacitance sensor 112.While the illustrated example of FIG. 1 depicts the first pressuresensor 104 within the pressure chamber 110 when the electrical tests arebeing conducted, the electrical tests may be performed when the firstpressure sensor 104 is disposed outside of the pressure chamber 110. Inother words, the physical tests of the training phase 102 may beperformed with the first pressure sensor 104 disposed within thepressure chamber 110 and the electrical tests of the training phase 102may be performed with the first pressure sensor 104 disposed inside oroutside of the pressure chamber 110. While the illustrated example ofFIG. 1 depicts the capacitance sensor 112 being used in both physicaland electrical testing, in other examples, separate capacitance sensorsare used.

In some examples, the electrical tests include the first voltagestimulator 120 applying a first voltage value 122 to and/or across thefirst pressure sensor 104 and the capacitance sensor 112 measuring theresultant second capacitance value(s) 124 based on the voltage(s)applied. In some examples, results 600 of the electrical tests areplotted on a graph 602 depicted in FIG. 6, where an x-axis 604represents voltage and a y-axis 606 represents capacitance.

Referring back to the example of FIG. 1, the first voltage stimulator120 and/or the capacitance sensor 112 provide or otherwise enable thecorrelator 118 to access the first voltage value(s) 122 and the secondcapacitance value(s) 124 for further processing and/or to determinecorrelation coefficient values 126 used when calibrating other pressuresensors. In some examples, the correlation coefficient value(s) 126 aredetermined for the different pressures by the correlator 118 based onthe measured pressure values 114, the first capacitance values 116, thefirst voltage values 122 and/or the second capacitance values 124 bygenerating correlation curves using, for example, a second orderpolynomial function such as, for example, Equation 3 above. In someexamples, correlation curves 700 generated by the correlator 118 areplotted on a graph 702 as depicted in FIG. 7, where an x-axis 704represents the capacitance in the electrical domain f (C_(v)) and ay-axis 706 represents the capacitance in the physical domain, f (C_(p)).

In this manner, in some examples, a range of voltages are applied to thefirst pressure sensor 104 by performing a voltage sweep on the firstpressure sensor 104 to enable the resultant second capacitance values124 output by the first pressure sensor 104 to be measured by thecapacitance sensor 112. As used herein, the phrase “voltage sweep”refers to applying a plurality of voltage values to a pressure sensorwhere the voltage values may be incrementally or otherwise spacedbetween a first voltage value (e.g., 0V) and a second voltage value(e.g., 3V). As shown in the example of FIG. 1, the correlationcoefficient value(s) and corresponding pressure value(s) 126 areprovided to a database 128 for storage.

FIG. 2 illustrates an example implementation of the correlator 118 ofFIG. 1. In the illustrated example, the correlator 118 includes anexample pressure/capacitance correlator 202, an example firstvoltage/capacitance correlator 204 and an examplepressure/voltage/capacitance correlator 206.

In the illustrated example, to process the measured pressure values 114and the first capacitance values 116 associated with the physical testsof the training phase 102, the pressure/capacitance correlator 202receives and/or accesses the measured pressure values 114 and the firstcapacitance values 116 and determines capacitance values 214 in thephysical domain, f (C_(p)), using, for example, Equation 1. In someexamples, the capacitance values 214 in the physical domain, f (C_(p)),account for the capacitance (e.g., C_(p) _(=1013 hpa) ) of the firstpressure sensor 104 at ambient pressure.

In the illustrated example, to process the first voltage values 122 andthe second capacitance values 124 associated with the electrical testsof the training phase 102, the voltage/capacitance correlator 204receives and/or accesses the first voltage values 122 and the secondcapacitance values 124 and determines capacitance values 216 in theelectrical domain, f (C_(v)) using, for example, Equation 2. In someexamples, the capacitance values 216 in the electrical domain, f(C_(v)), account for the capacitance, C_(min), of the first pressuresensor 104 when voltage is not being applied to the first pressuresensor 104 and/or the capacitance, C_(min), of the first pressure sensor104 when a minimum voltage is being applied to the first pressure sensor104.

In the illustrated example, to determine the correlation coefficientvalues 126 used to calibrate other pressure sensors, thepressure/voltage/capacitance correlator 206 receives and/or accesses thecapacitance values 214 in the physical domain, f (C_(p)), and thecapacitance values 216 in the electrical domain, f (C_(v)), anddetermines the correlation coefficient values 126 for each of thepressure values having a corresponding capacitance value 214 in thephysical domain, f (C_(p)), using, for example, Equation 3. In someexamples, to associate the correlation coefficient values 126 with acorresponding pressure value, the pressure/voltage/capacitancecorrelator 206 generates a look-up table in which the correlationcoefficient values 126 (e.g., b₁, b₂, b₃) are associated with arespective pressure value (e.g., P₁, P₂, P₃, etc.).

FIG. 3 illustrates an example calibration system 300 that can be used tocalibrate micro-electromechanical systems (MEMS) including pressuresensors in a cost effective and efficient manner. In the illustratedexample, the calibration system 300 includes an example testing phase302 that calibrates a second pressure sensor 304 using the determinedcorrelation coefficient values 126 and the results of electrical testsconducted on the second pressure sensor 304. While the illustratedexample depicts one pressure sensor (i.e., the second pressure senor304) in the testing phase 302, in other examples, any number of pressuresensors may be used during the testing phase 302.

In some examples, the electrical tests include a second voltagestimulator 306 applying second voltage values 308 to and/or across thesecond pressure sensor 304 and a capacitance sensor 310 measuringresultant third capacitance values 312 based on the voltage(s) applied.Instead of performing a full voltage sweep on the second pressure sensor304 during the testing phase 302, in some examples, the testing phase302 includes applying first and second voltage values (e.g., 0V, 3V) tothe second pressure sensor 304 and determining the third capacitancevalue(s) 312.

In the illustrated example, the second voltage stimulator 306 and thecapacitance sensor 310 provide or otherwise enable a calibrator 314 toaccess the second voltage values 308 and the third capacitance values312 for further processing. In some examples, the further processingincludes the calibrator 314 determining calibration coefficient values316 that can be used to calibrate the second pressure sensor 304 and/orstored on a data store 318 of the second pressure sensor 304. Thecalibration coefficient values 316 may be determined based on theelectrical tests performed on the second pressure sensor 304, thecorrelation coefficient value(s) 126 from the correlator 118, pressuresensor data and/or associated parameters 320 from a database 322 and/oran ambient pressure value(s) 324 measured by a fifth sensor and/orpressure gauge 326.

In some examples, the pressure sensor data and/or associated parameters320 include, for example, a plate area of the second pressure sensor304, A_(p), a plate radius of the second pressure sensor 304, a, apermittivity of the free space within the second pressure sensor 304,ε₀, a relative permittivity of an oxide of the second pressure sensor304, ε_(r,ox) and/or a peak plate displacement of the second pressuresensor 304, x_(p). Additionally and/or alternatively, in some examples,the pressure sensor data and/or associated parameters 320 include, forexample, a displacement adjustment of the second pressure sensor 304,δx_(p), an effective gap of the second pressure sensor 304, g₀, an airgap of the second pressure sensor 304, g_(noox), a thickness of theoxide of the second pressure sensor 304, t_(ox), a parasitic offset ofthe second pressure sensor 304, C_(par), flexural rigidity of the secondpressure sensor 304, D, Young's modulus, E and/or Poisson's ratio, v.

FIG. 4 illustrates an example implementation of the calibrator 314 ofFIG. 3. In the illustrated example, the calibrator 314 includes anexample re-constructor 402, an example data fitter 404 and an exampledeterminer 406. In the illustrated example, to determine the resultantcapacitance values when the second pressure sensor 304 is exposed todifferent pressures without actually performing physical tests on thesecond pressure sensor 304, the re-constructor 402 accesses and/orreceives the correlation coefficient values 126 and correspondingpressure values, the third capacitance value(s) 312, the ambientpressure value 324 and the second voltage value(s) 308 and predictsresultant capacitances 408 that the second pressure sensor 304 wouldgenerate if the second pressure sensor 304 were actually exposed todifferent pressures using Equations 3 and/or 4. In some examples, there-constructor 402 uses Equation 3 to account for the capacitance of thesecond pressure sensor 304 in the electrical domain when voltage is notbeing applied to the second pressure sensor 304 and uses Equation 4 topredict the capacitance that the second pressure sensor 304 wouldgenerate if the second pressure sensor 304 were actually exposed todifferent pressures. Thus, by selecting the correlation coefficientvalues 126 associated with a respective pressure, the examplere-constructor 402 can predict the capacitance values in the physicaldomain for the second pressure sensor 304 without actually performingphysical tests on the second pressure sensor 304.

To determine other and/or extrapolate capacitance and pressure values410 determined by the re-constructor 402, in the illustrated example,the data fitter 404 accesses the pressure sensor data and/or associatedparameters 320 and the pressure and capacitance values 408 anddetermines extrapolates and/or fits other pressure and capacitancevalues 410 using the sensor equation fit of Equation 5 and places thedata in a simpler form using the 5^(th) order polynomial equation ofEquation 9.

To determine the calibration coefficient values 316 to be used tocalibrate the second pressure sensor 304, the determiner 406 accessesother pressure and capacitance values 410 from the data fitter 404 andprocesses the other pressure and capacitance values 410 to determine thecalibration coefficient values 316. Thus, using the examples disclosedherein, the example correlator 118 determines the correlationcoefficient values 126 by performing physical and electrical tests onthe first pressure sensor 104 and the example calibrator 314 determinesthe calibration coefficient values 316 based on the correlationcoefficient values 126 and electrical tests performed on the secondpressure sensor 304. In some examples, the calibration coefficientvalues 316 are stored in a memory to be later used to calibrate eachsensor individually.

While an example manner of implementing the example correlator 118 ofFIG. 1 is illustrated in FIG. 2 and an example of implementing theexample calibrator 314 of FIG. 3 is illustrated in FIG. 4, one or moreof the elements, processes and/or devices illustrated in FIGS. 2 and/or4 may be combined, divided, re-arranged, omitted, eliminated and/orimplemented in any other way. Further, the example pressure/capacitancecorrelator 202, the example first voltage/capacitance correlator 204,the example pressure/voltage/capacitance correlator 206, the examplecorrelator 118, the example re-constructor 402, the example data fitter404, the example determiner 406 and/or the example calibrator 314 ofFIGS. 2 and/or 4 may be implemented by hardware, software, firmwareand/or any combination of hardware, software and/or firmware. Thus, forexample, any of the example pressure/capacitance correlator 202, theexample first voltage/capacitance correlator 204, the examplepressure/voltage/capacitance correlator 206, the example correlator 118,the example re-constructor 402, the example data fitter 404, the exampledeterminer 406 and/or the example calibrator 314 of FIGS. 2 and/or 4could be implemented by one or more analog or digital circuit(s), logiccircuits, programmable processor(s), application specific integratedcircuit(s) (ASIC(s)), programmable logic device(s) (PLD(s)) and/or fieldprogrammable logic device(s) (FPLD(s)). When reading any of theapparatus or system claims of this patent to cover a purely softwareand/or firmware implementation, at least one of the examplepressure/capacitance correlator 202, the example firstvoltage/capacitance correlator 204, the examplepressure/voltage/capacitance correlator 206, the example correlator 118,the example re-constructor 402, the example data fitter 404, the exampledeterminer 406 and/or the example calibrator 314 is/are hereby expresslydefined to include a tangible computer readable storage device orstorage disk such as a memory, a digital versatile disk (DVD), a compactdisk (CD), a Blu-ray disk, etc. storing the software and/or firmware.Further still, the example correlator 118 and the calibrator 314 ofFIGS. 1 and 3 may include one or more elements, processes and/or devicesin addition to, or instead of, those illustrated in FIGS. 2 and 4,and/or may include more than one of any or all of the illustratedelements, processes and devices.

FIG. 5 illustrates the example graph 502 including resultantcapacitances of the first pressure sensor 104 being exposed to differentpressures during the training phase 102 and/or predictedcapacitance/pressure combinations for the second pressure sensor 304 inthe testing phase 302. The graph 502 of FIG. 5 includes the x-axis 504that represents pressure and the y-axis 506 that represents capacitance.

FIG. 6 illustrates the example graph 602 including resultantcapacitances of the first pressure sensor 104 being exposed to differentvoltages during the training phase 102 and/or predictedcapacitance/voltage combinations for the second pressure sensor 304 inthe testing phase 302. The graph 602 of FIG. 6 includes the x-axis 604that represents voltage and the y-axis 606 that represents capacitance.

FIG. 7 illustrates the example graph 702 including the correlationcurves 700 generated using Equation 4 where the x-axis 704 representsthe capacitance in the electrical domain f (C_(v)) and the y-axis 706represents the capacitance in the physical domain, f (C_(p)).

Flowcharts representative of example machine readable instructions forimplementing the example correlator 118 and the example calibrator 314of FIGS. 1-4 are shown in FIGS. 8-10. In this example, the machinereadable instructions comprise a program for execution by a processorsuch as the processors 1112, 1212 shown in the example processorplatforms 1100, 1200 discussed below in connection with FIGS. 11, 12.The program may be embodied in software stored on a tangible computerreadable storage medium such as a CD-ROM, a floppy disk, a hard drive, adigital versatile disk (DVD), a Blu-ray disk, or a memory associatedwith the processor 1112, 1212, but the entire program and/or partsthereof could alternatively be executed by a device other than theprocessor 1112, 1212 and/or embodied in firmware or dedicated hardware.Further, although the example program is described with reference to theflowchart illustrated in FIGS. 8-10, many other methods of implementingthe example correlator 118 and the example calibrator 314 mayalternatively be used. For example, the order of execution of the blocksmay be changed, and/or some of the blocks described may be changed,eliminated, or combined.

As mentioned above, the example processes of FIGS. 8-10 may beimplemented using coded instructions (e.g., computer and/or machinereadable instructions) stored on a tangible computer readable storagemedium such as a hard disk drive, a flash memory, a read-only memory(ROM), a compact disk (CD), a digital versatile disk (DVD), a cache, arandom-access memory (RAM) and/or any other storage device or storagedisk in which information is stored for any duration (e.g., for extendedtime periods, permanently, for brief instances, for temporarilybuffering, and/or for caching of the information). As used herein, theterm tangible computer readable storage medium is expressly defined toinclude any type of computer readable storage device and/or storage diskand to exclude propagating signals and to exclude transmission media. Asused herein, “tangible computer readable storage medium” and “tangiblemachine readable storage medium” are used interchangeably. Additionallyor alternatively, the example processes of FIGS. 8-10 may be implementedusing coded instructions (e.g., computer and/or machine readableinstructions) stored on a non-transitory computer and/or machinereadable medium such as a hard disk drive, a flash memory, a read-onlymemory, a compact disk, a digital versatile disk, a cache, arandom-access memory and/or any other storage device or storage disk inwhich information is stored for any duration (e.g., for extended timeperiods, permanently, for brief instances, for temporarily buffering,and/or for caching of the information). As used herein, the termnon-transitory computer readable medium is expressly defined to includeany type of computer readable storage device and/or storage disk and toexclude propagating signals and to exclude transmission media. As usedherein, when the phrase “at least” is used as the transition term in apreamble of a claim, it is open-ended in the same manner as the term“comprising” is open ended.

The program of FIG. 8 begins with the correlator 118 determiningcorrelation coefficient values 126 for different pressure values (block802). In some examples, the correlation coefficient values 126 aredetermined based on first values 114, 116, 122 and/or 124 determinedduring first tests on the first sensor 104. The calibrator 314determines calibration coefficient values 316 to be used to calibratethe second sensor 304 (block 804). In some examples, the calibrationcoefficient values 316 are determined based on second values 308, 312,324 and/or 320 and the correlation coefficient values 126. Thecalibration coefficient values 316 are stored on the second pressuresensor 304 (block 806).

FIG. 9 illustrates an example of performing the processes of block 802to determine the correlation coefficient values 126. The program of FIG.9 begins with the pressure/capacitance correlator 202 accessing themeasured pressure values 114 (block 902) and the first capacitancevalues 116 (block 904) from the physical tests performed on the firstpressure sensor 104 during the training phase 102. Thepressure/capacitance correlator 202 processes the measured pressurevalues 114 and the first capacitance values 116 using, for example,Equation 1, to determine the capacitance values 214 in the physicaldomain, f (C_(p)) (block 906).

The first voltage/capacitance correlator 204 accesses the first voltagevalues 122 (block 908) and the second capacitance values 124 (block 910)from the electrical tests performed on the first pressure sensor 104.The voltage/capacitance correlator 204 processes the first voltagevalues 122 and the second capacitance values 124 using, for example,Equation 2, to determine the capacitance values 216 in the electricaldomain, f (C_(v)) (block 912).

The pressure/voltage/capacitance correlator 206 processes thecapacitance values 214 in the physical domain, f (C_(p)) and thecapacitance values 216 in the electrical domain, f (C_(v)) to determinethe correlation coefficient values 126 for each of the pressure valueshaving a corresponding capacitance value in the physical domain, f(C_(p)), 214, using, for example, Equation 3 (block 914). The database128 stores the correlation coefficient values 126 and the associatedpressure values in the database 128 (block 916). The process thenreturns to FIG. 8.

FIG. 10 illustrates an example of performing the processes of block 804to determine the calibration coefficient values 316 for the secondsensor 304. The program of FIG. 10 begins with the re-constructor 402 ofthe calibrator 314 accessing the third capacitance values 312 (block1002) from the electrical tests performed on the second pressure sensor304. The re-constructor 402 selects a pressure value to predict theresultant capacitance value that the second pressure sensor 304 wouldgenerate if the second pressure sensor 304 were actually physicallyexposed to the selected pressure (block 1004). The re-constructor 402identifies and/or selects the associated correlation coefficient values126 associated with the selected pressure from, for example, a look-uptable generated by the pressure/voltage/capacitance correlator 206(block 1006).

To predict the resultant capacitance values in the physical domain forthe second pressure sensor 304, the re-constructor 402 processes thecorrelation coefficient values 126 for the selected pressure, the thirdcapacitance value(s) 312, the ambient pressure value 324 and/or thesecond voltage value(s) 308 and determines the capacitance value 410 forthe selected pressure (block 1008). The database 322 stores theassociated pressure and capacitance values 410 in the database 322(block 1010). If another pressure is selected at block 1012, controladvances to block 1014.

However, if another pressure is not selected at block 1012, the datafitter 404 accesses the pressure and capacitance values 214 and/or thepressure sensor data and/or associated parameters 320 and determinesother values, extrapolates and/or fits the pressure and capacitancevalues 410 using an example sensor equation fit and/or places the datain a simpler form using an example 5^(th) order polynomial fit equation(block 1016).

The determiner 406 determines the calibration coefficient values 316 tobe used to calibrate the second pressure sensor 304 by processing theother pressure and capacitance values 410 to determine the calibrationcoefficient values 316 (block 1018). The process then returns to FIG. 8.

The processor platform 1100 of the illustrated example includes aprocessor 1112. The processor 1112 of the illustrated example ishardware. For example, the processor 1112 can be implemented by one ormore integrated circuits, logic circuits, microprocessors or controllersfrom any desired family or manufacturer. In this example, the processor1112 implements the example pressure/capacitance correlator 202, theexample first voltage/capacitance correlator 204, the examplepressure/voltage/capacitance correlator 206 and the example correlator118.

The processor 1112 of the illustrated example includes a local memory1113 (e.g., a cache). The processor 1112 of the illustrated example isin communication with a main memory including a volatile memory 1114 anda non-volatile memory 1116 via a bus 1118. The volatile memory 1114 maybe implemented by Synchronous Dynamic Random Access Memory (SDRAM),Dynamic Random Access Memory (DRAM), RAMBUS Dynamic Random Access Memory(RDRAM) and/or any other type of random access memory device. Thenon-volatile memory 1116 may be implemented by flash memory and/or anyother desired type of memory device. Access to the main memory 1114,1116 is controlled by a memory controller.

The processor platform 1100 of the illustrated example also includes aninterface circuit 1120. The interface circuit 1120 may be implemented byany type of interface standard, such as an Ethernet interface, auniversal serial bus (USB), and/or a PCI express interface.

In the illustrated example, one or more input devices 1122 are connectedto the interface circuit 1120. The input device(s) 1122 permit(s) a userto enter data and commands into the processor 1112. The input device(s)can be implemented by, for example, an audio sensor, a microphone, acamera (still or video), a keyboard, a button, a mouse, a touchscreen, atrack-pad, a trackball, isopoint and/or a voice recognition system.

One or more output devices 1124 are also connected to the interfacecircuit 1120 of the illustrated example. The output devices 1124 can beimplemented, for example, by display devices (e.g., a light emittingdiode (LED), an organic light emitting diode (OLED), a liquid crystaldisplay, a cathode ray tube display (CRT), a touchscreen, a tactileoutput device, a light emitting diode (LED)). The interface circuit 1120of the illustrated example, thus, typically includes a graphics drivercard, a graphics driver chip or a graphics driver processor.

The interface circuit 1120 of the illustrated example also includes acommunication device such as a transmitter, a receiver, a transceiver, amodem and/or network interface card to facilitate exchange of data withexternal machines (e.g., computing devices of any kind) via a network1126 (e.g., an Ethernet connection, a digital subscriber line (DSL), atelephone line, coaxial cable, a cellular telephone system, etc.).

The processor platform 1100 of the illustrated example also includes oneor more mass storage devices 1128 for storing software and/or data.Examples of such mass storage devices 1128 include floppy disk drives,hard drive disks, compact disk drives, Blu-ray disk drives, RAIDsystems, and digital versatile disk (DVD) drives.

The coded instructions 1132 of FIGS. 8-10 may be stored in the massstorage device 1128, in the volatile memory 1114, in the non-volatilememory 1116, and/or on a removable tangible computer readable storagemedium such as a CD or DVD.

The processor platform 1200 of the illustrated example includes aprocessor 1212. The processor 1212 of the illustrated example ishardware. For example, the processor 1212 can be implemented by one ormore integrated circuits, logic circuits, microprocessors or controllersfrom any desired family or manufacturer. In this example, the processor1212 implements the example re-constructor 402, the example data fitter404, the example determiner 406 and the example calibrator 314.

The processor 1212 of the illustrated example includes a local memory1213 (e.g., a cache). The processor 1212 of the illustrated example isin communication with a main memory including a volatile memory 1214 anda non-volatile memory 1216 via a bus 1218. The volatile memory 1214 maybe implemented by Synchronous Dynamic Random Access Memory (SDRAM),Dynamic Random Access Memory (DRAM), RAMBUS Dynamic Random Access Memory(RDRAM) and/or any other type of random access memory device. Thenon-volatile memory 1216 may be implemented by flash memory and/or anyother desired type of memory device. Access to the main memory 1214,1216 is controlled by a memory controller.

The processor platform 1200 of the illustrated example also includes aninterface circuit 1220. The interface circuit 1220 may be implemented byany type of interface standard, such as an Ethernet interface, auniversal serial bus (USB), and/or a PCI express interface.

In the illustrated example, one or more input devices 1222 are connectedto the interface circuit 1220. The input device(s) 1222 permit(s) a userto enter data and commands into the processor 1212. The input device(s)can be implemented by, for example, an audio sensor, a microphone, acamera (still or video), a keyboard, a button, a mouse, a touchscreen, atrack-pad, a trackball, isopoint and/or a voice recognition system.

One or more output devices 1224 are also connected to the interfacecircuit 1220 of the illustrated example. The output devices 1224 can beimplemented, for example, by display devices (e.g., a light emittingdiode (LED), an organic light emitting diode (OLED), a liquid crystaldisplay, a cathode ray tube display (CRT), a touchscreen, a tactileoutput device, a light emitting diode (LED)). The interface circuit 1220of the illustrated example, thus, typically includes a graphics drivercard, a graphics driver chip or a graphics driver processor.

The interface circuit 1220 of the illustrated example also includes acommunication device such as a transmitter, a receiver, a transceiver, amodem and/or network interface card to facilitate exchange of data withexternal machines (e.g., computing devices of any kind) via a network1226 (e.g., an Ethernet connection, a digital subscriber line (DSL), atelephone line, coaxial cable, a cellular telephone system, etc.).

The processor platform 1200 of the illustrated example also includes oneor more mass storage devices 1228 for storing software and/or data.Examples of such mass storage devices 1228 include floppy disk drives,hard drive disks, compact disk drives, Blu-ray disk drives, RAIDsystems, and digital versatile disk (DVD) drives.

The coded instructions 1232 of FIGS. FIGS. 8-10 may be stored in themass storage device 1228, in the volatile memory 1214, in thenon-volatile memory 1216, and/or on a removable tangible computerreadable storage medium such as a CD or DVD.

From the foregoing, it will be appreciated that the above disclosedmethods, apparatus and articles of manufacture relate to calibratingmicro-electromechanical systems (MEMS) such as, for example, pressuresensors and/or capacitive based barometric pressure sensors.Specifically, the examples disclosed herein relate to performing testson first pressure sensors during a training phase and calibrating secondpressure sensors during a testing phase using correlation coefficientvalues determined during the training phase. By taking such an approach,the examples disclosed herein enable the efficient calibration of alarge quantity of pressure sensors based on calibration coefficientvalues determined by testing a lesser number of pressure sensors.

Although certain example methods, apparatus and articles of manufacturehave been disclosed herein, the scope of coverage of this patent is notlimited thereto. On the contrary, this patent covers all methods,apparatus and articles of manufacture fairly falling within the scope ofthe claims of this patent.

What is claimed is:
 1. A pressure sensor calibration apparatus,comprising: a correlator having a correlator input and a correlatoroutput, the correlator input adapted to be coupled to a source of firstand second capacitance values, the correlator configured to determinecorrelation coefficient values based on the first and second capacitancevalues and to output the correlation coefficient values at thecorrelator output, the first capacitance value determined during aphysical test on a first pressure sensor, the second capacitance valuedetermined during a first electrical test on the first pressure sensor,the physical test including exposing the first pressure sensor to afirst pressure and determining the first capacitance value based on thefirst pressure applied, and the first electrical test including exposingthe first pressure sensor to a first voltage and determining the secondcapacitance value based on the first voltage applied; and a calibratorhaving first and second calibrator inputs, the first calibrator inputadapted to be coupled to the correlator output, the second calibratorinput adapted to be coupled to a source of a third capacitance value,the calibrator configured to determine calibration coefficient valuesbased on the correlation coefficient values and the third capacitancevalue, the third capacitance value determined during a second electricaltest on a second pressure sensor, and the second electrical testincluding exposing the second pressure sensor to a second voltage anddetermining the third capacitance value based on the second voltageapplied.
 2. The pressure sensor calibration apparatus of claim 1,wherein the correlator includes a pressure/capacitance correlatorconfigured to process the first capacitance value to determine a fourthcapacitance value that accounts for a minimum capacitance at ambientpressure, and the correlator is configured to use the fourth capacitancevalue to determine the correlation coefficient values.
 3. The pressuresensor calibration apparatus of claim 1, wherein the correlator includesa voltage/capacitance correlator configured to process the secondcapacitance value to determine a fourth capacitance value that accountsfor a minimum voltage applied to the first pressure sensor, and thecorrelator is configured to use the fourth capacitance value todetermine the correlation coefficient values.
 4. The pressure sensorcalibration apparatus of claim 1, wherein the calibrator is configuredto determine the calibration coefficient values to calibrate the secondpressure sensor without performing physical tests on the second pressuresensor.
 5. The pressure sensor calibration apparatus of claim 1, whereinthe calibrator includes a re-constructor configured to predict a fourthcapacitance value for the second pressure sensor without performingphysical tests on the second pressure sensor.
 6. The pressure sensorcalibration apparatus of claim 1, wherein the calibrator is configuredto determine calibration coefficient values for a plurality of pressuresensors including the second pressure sensor.
 7. The pressure sensorcalibration apparatus of claim 1, wherein the correlator is configuredto generate a table to associate the correlation coefficient values andthe first pressure.
 8. A method of calibrating a pressure sensor, themethod comprising: by executing at least one instruction with at leastone processor: determining correlation coefficient values based on afirst capacitance value determined during a physical test on a firstpressure sensor and a second capacitance value determined during a firstelectrical test on the first pressure sensor; and determiningcalibration coefficient values to calibrate a second pressure sensorbased on the correlation coefficient values and a third capacitancevalue determined during a second electrical test on the second pressuresensor.
 9. The method of claim 8, wherein the physical test includesexposing the first pressure sensor to a first pressure and determiningthe first capacitance value based on the first pressure applied, and thefirst electrical test includes exposing the first pressure sensor to afirst voltage and determining the second capacitance value based on thefirst voltage applied.
 10. The method of claim 8, wherein the secondelectrical test includes exposing the second pressure sensor to a secondvoltage and determining the third capacitance value based on the secondvoltage applied.
 11. The method of claim 8, wherein the determining ofthe correlation coefficient values includes processing the firstcapacitance value to determine a fourth capacitance value that accountsfor a minimum capacitance at ambient pressure and using the fourthcapacitance value to determine the correlation coefficient values. 12.The method of claim 8, wherein the determining of the calibrationcoefficient values includes predicting a fourth capacitance value forthe second pressure sensor without performing physical tests on thesecond pressure sensor.
 13. The method of claim 8, wherein the physicaltest includes exposing the first pressure sensor to a first pressure,and the method further comprises generating a table to associate thecorrelation coefficient values and the first pressure.
 14. The method ofclaim 8, further comprising storing the calibration coefficient valueson the second pressure sensor.
 15. A tangible machine-readable storagedisk or storage device comprising instructions which, when executed,cause a machine to at least: determine correlation coefficient valuesbased on a first capacitance value determined during a physical test ona first pressure sensor and a second capacitance value determined duringa first electrical test on the first pressure sensor; and determinecalibration coefficient values to calibrate a second pressure sensorbased on the correlation coefficient values and a third capacitancevalue determined during a second electrical test on the second pressuresensor.
 16. The machine-readable storage disk or device of claim 15,wherein the instructions, when executed, further cause the machine tostore the calibration coefficient values on the second pressure sensor.17. The machine-readable storage disk or device of claim 15, wherein thephysical test includes exposing the first pressure sensor to a firstpressure and determining the first capacitance value based on the firstpressure applied, and the first electrical test includes exposing thefirst pressure sensor to a first voltage and determining the secondcapacitance value based on the first voltage applied.
 18. Themachine-readable storage disk or device of claim 15, wherein the secondelectrical test includes exposing the second pressure sensor to a secondvoltage and determining the third capacitance value based on the secondvoltage applied.
 19. The machine-readable storage disk or device ofclaim 15, wherein the determining of the calibration coefficient valuesincludes processing the first capacitance value to determine a fourthcapacitance value that accounts for a minimum capacitance at ambientpressure and using the fourth capacitance value to determine thecorrelation coefficient values.
 20. The machine-readable storage disk ordevice of claim 15, wherein the determining of the calibrationcoefficient values includes predicting a fourth capacitance value forthe second pressure sensor without performing physical tests on thesecond pressure sensor.